Indeed, I have seen shared hosting with 1,000+ SQL Server databases hum along without any problems and others with only a few that were "overloaded" because of intense query volumes and lots of computed columns. It all depends on what those databases are doing and what the load is like,
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Justin ScottDec 23 '09 at 3:03

The most I've ever seen on sql server instance was 3500 databases, just shy of a petabyte total data. It was interesting to see a windows sql cluster with a dedicated SAN. On a side note there was also an analysis services cluster with it's own dedicated san as well. I have no idea how many cubes were on that instance.

As I rarely deal with mysql (I've only done migrations from mysql to sql server) and have never dealt with postgres I can't comment on scalability of those platforms. The biggest mysql server I've seen was 10 DBs with about 4 terabytes of data total.